Gas diffusers designed to produce fine gas bubbles in a body of liquid through the process of bubble shearing have been known for some time. U.S. Pat. No. 3,650,513 issued to Werner on March 21, 1972 provides one of the most recent examples of such bubble shearing apparatus, in the form of a rotating disk with porous surfaces on both the top and the bottom of the disk.
Three embodiments of a rotating gas diffuser are disclosed in side elevation or cross section in FIGS. 1, 2 and 8 of the Werner patent just referred to. The ratio of the disk diameter to maximum disk thickness in the gas diffusing area in these embodiments is approximately 15:1, 13:1 and 16:1, respectively as taken from the drawings. It was evidently believed that these ratios of disk diameter to thickness were preferred ratios representing the best mode contemplated by the inventor for carrying out his invention, despite the fact that it has been known for a long time that extremely thin solid disks are preferred if it is desired to reduce the parasitic drag on such a disk due to the vertically oriented edge surface of the disk when it is rotated in a body of liquid in which it is immersed.
Apparently it was believed that replacing the vertically oriented edge surface of the rotating disk with a tapered annular portion, as shown in the Werner patent, would reduce the parasitic drag to which the disk is subjected enough to make it unnecessary to employ a thin disk to reduce that drag, and thus would avoid the structural problems of providing a disk of such dimensions. It may even have been believed that it was not possible to use a thin rotating disk in bubble shearing apparatus because it was assumed that a typical gas plenum--together with any porous plates thick enough to avoid cracking under the forces that would be exerted if it was decided to introduce gas into the plenum at relatively high pressure, as well as under the other stresses of ordinary use--would occupy so much space as to make it necessary to have a relatively thick rotating disk such as disclosed in the various figures of the prior art patent referred to. Or it may have been believed necessary to employ a deeper plenum than has now been found necessary, in order to assure the uniform distribution of gas pressure within the plenum, with a resulting uniform gas flow throughout the entire area of the porous diffusing surface.
This reluctance to use a thin rotating disk in bubble shearing apparatus might have been overcome if there had been any recognition in the prior art of the harmful effect on the ultimate size of the bubbles derived from the use of a rotating disk gas diffuser of the vortices that are shed at the edge of the rotating disk and embedded in the turbulent wake and jet flowing outward from the disk. But so far as the prior art shows, there was no recognition of this harmful effect until the instant invention was made.
The basic hydrodynamics of the formation of the wake and jet moving radially outward from the edge of a rotating disk has been well known for some time. This phenomenon results basically from the fact that when a disk is rotated in a liquid in which it is immersed, the drag of the rotating disk on the liquid adjacent the disk produces a boundary layer flow at the top and bottom surfaces of the rotating disk. The thickness of the boundary layer, that is, the thickness of the transition zone from the liquid moving at the speed of the disk to the main body of liquid that is virtually still, is generally quite thin in comparison to the diameter of the disk.
The boundary layer flow is not a purely tangentially directed flow, but contains a component directed radially outward that is created by the centrifugal force resulting from the rotation of the disk. As the upper and lower boundary layers spiral off the top and bottom surfaces of the rotating disk, they form a wake at the disk edge that in turn is transformed into a spiraling jet that moves radially away from the disk. The wake and the jet are generally turbulent flows, but they are not entirely free of structure in the vicinity of the disk. For one thing, the two boundary layers tend to be parallel flows separated by the thickness of the disk. For another, the liquid motion created between the two boundary layers triggers swirling motions that develop into large vortices attached to the edge of the disk.
Periodically these vortices are shed from the disk, and spiral outward with the boundary layer flow like miniature tornadoes. As a result, these "tornadoes" entrain large quantities of bulk liquid at the edges of the wake and the jet, until the vortices dissipate in the jet. The entrainment of previously quiescent liquid in the jets causes the jet flow to grow to ten or twenty times the magnitude of the boundary layer flows. This entrainment--produced as it is by vortices that are of relatively large size in comparison to the size of turbulent eddies--is frequently referred to as "large scale entrainment."
For representative discussions in the prior art illustrating the growing understanding over the years of the nature of the boundary layer on the surface of a rotating disk, see von Karman, T., "On Laminar and Turbulent Friction," Zeitschrift fur Angerwandte Mathematik und Mechanik, 1 (1921) pp. 233-252 (Translation: NACA TM 1092 (1945), especially pages 20-30); Gregory, N., Stuart, J. T. and Walker, W. S., "On the Stability of Three-dimensional Boundary Layers with Application to the Flow Due to a Rotating Disk," Phil. Trans. A 248 (1955) pp. 155-199; Cham, T. S., and Head, M. R., "Turbulent Boundary Layer Flow on a Rotating Disk," Journal of Fluid Mechanics, 37 (1969)pp. 129-147; and Cooper, P., "Turbulent Boundary Layer on a Rotating Disk Calculated with an Effective Viscosity," AIAA Journal, 9 (1971) pp. 255-261.
For the growing understanding up to 1971 of the basic hydrodynamics of the development and breaking off of vortices from various solid bodies moving through a liquid, with some recognition of the resulting large scale entrainment of quiescent liquid, see Chanaud, R. C., "Measurements of Mean Flow Velocity Beyond a Rotating Disk," Journal of Basic Engineering, Transactions ASME, Series D, 93 (1971) pp. 199-204 and discussion by P. D. Richardson, p. 204; and Bevilaqua, P. M., and Lykoudis, P. S., "Mechanism of Entrainment in Turbulent Wakes," AIAA Journal, 9 (1971) pp. 1657-1659.
Knowledge of the general principles of hydrodynamics that begin to explain the development of the wake and jet at the edges of a rotating disk has not, however, led prior workers in the field to examine the various detailed factors relating to that phenomenon and to the effect of the wake and jet on the size of the bubbles that are dispersed outwardly from a rotating gas diffuser and then rise through the body of liquid. Among these factors are (1) the number of vortices produced by the rotation of the disk, (2) the size and spacing of the vortices, (3) the velocity of movement of the vortices radially outward with respect to the rotating disk, (4) the pressure differential between the interior and exterior of individual vortices, (5) the thickness of the resulting wake and jet, (6) the rate of decay of the vortices through viscous dissipation, (7) the transport of bubbles from the turbulent wake/jet into the interior of the vortices, (8) the coalescence of bubbles in the interior of the vortices, (9) the effect of the spacing between bubbles on the number of bubbles coalesced in the interior of the vortices, (10) the comparison of bubble coalescence in the small scale turbulent eddies present in the wake and jet with the coalescence taking place inside the vortices, (11) the comparison of the rate of bubble coalescence in the vortices created in the transition from laminar to turbulent flow on the surface of the rotating disk with the rate of bubble coalescence in the vortices shed from the edges of the disk, and (12) the comparison of the size of the bubbles sheared from the surface of the disk with the size of the bubbles rising from the turbulent wake or jet at the edge of the rotating disk.
If the effect of the disk thickness on these various detailed factors (whether taken separately, all together, or in any combination of the various factors) had been examined by prior art workers, this work might possibly have led to an understanding of the effect of the vortices shed from the edges of a rotating disk member upon the size of the bubbles produced by bubble shearing with a rotating gas diffuser, which might conceivably in turn have suggested the desirability of using a very thin disk like member in such a gas diffuser. But no such work was ever done, and the indicated impact of disk thickness on bubble size was apparently wholly unsuspected until the present invention was made.
As a matter of fact, certain work reflected in the papers referred to above actually led away from the present invention because those papers emphasized the presence of large scale entrainment of quiescent liquid caused specifically by vortices generated at the transition from laminar to turbulent boundary layer flow on the surface of the rotating disk, and this particular type of production of vortices is of course independent of the thickness of the disk. This emphasis may as a practical matter have led prior art workers away from consideration of the effect of disk thickness on the size of the bubbles resulting from the use of a rotating gas diffuser, insofar as that bubble size is affected by the shedding of vortices at the edges of the rotating disk, which is the central question to which the present invention is addressed.